The former Liverpool and Newcastle striker succeeds Robert Page as new Wales coach.
Bellamy leaves his position as assistant manager at Burnley to take charge. He has signed a four-year contract.
"It's an incredible honour for me to be given the opportunity to lead my country and it's the proudest moment of my career," said Bellamy.
"It was always my ultimate dream to become the Cymru head coach and I am ready for the challenge.
"I will give my full commitment to develop this team and I am passionate to bring continued success into Welsh football. I can't wait to get started with our Nations League games in September."
Burnley chairman Alan Pace said: "I want to thank Craig for all his hard work during his time at Burnley and wish him the best for his new position as Wales manager.
"Craig has been a very important part of our wonderful journey the last two years. I've admired his leadership, knowledge and passion.
"I am certain that he will continue to find success in his new role, and I wish him the very best of luck."